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Abstract

The standard dyadic Green function description of the electromagnetic field generated by an electric point dipole is modified (and corrected) so that a rigorous classical theory for the attached and radiated parts of the near field appears. The present propagator formalism follows from analysis of the transverse and longitudinal dipole electrodynamics. Elimination of both the transverse and the longitudinal self-fields leads to a description of the radiated dipole field that enables one to obtain the associated energy flux in the near- and mid-field zones also and that is correctly retarded (with the vacuum speed of light) everywhere in space. The related retarded transverse propagator exists in the time (space) domain, whereas the standard propagator exists only in the frequency (space) domain. As a forerunner to an analysis of the Weyl expansions for the standard, longitudinal self-field and retarded transverse propagators, the plane-wave mode expansions of these propagators are investigated, and contour integrations are specified in such a manner that the rigorous Green function description is regained. It is found that, in order for the retarded transverse propagator description to be consistent in the near-field zone, the Weyl expansion for this propagator has to contain evanescent components not only for wave numbers larger than the vacuum wave number but in the entire angular spectrum. The present theory may influence our view of optical near-field phenomena and (classical) photon tunneling because in both of these fields a proper identification of attached and radiated fields seems needed.

References

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Table 1

Schematic Exposition Indicating Whether Propagating and Evanescent Modes Are Present in the Weyl Expansions of the Standard (D↔0), Longitudinal Self-Field (g↔L), and Retarded Transverse (D↔0T) Propagators in the Two Angular Spectral Regions 0<q‖⩽q0(=ω/c0) and q0<q‖<∞a

Propagator

Spectral Region

0⩽q‖⩽q0

q0<q‖<∞

D↔0

PROP

EVAN

g↔L

EVAN

EVAN

D↔0T

PROP+EVAN

EVAN

a PROP, propagating; EVAN, evanescent. The g↔L propagator contains only evanescent modes because the speed of light (c0) does not enter the dipole-attached field. To ensure that all nonretarded (with c0) phenomena are eliminated, D↔0T necessarily must contain an evanescent contribution also for 0⩽q‖⩽q0.